Talk:Frobenius theorem

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Yet another Frobenius theorem![edit]

This one can be stated in the language of permutation groups as:

If G is a transitive subgroup of the symmetric group S_{n} in which the only permutation with more than 1 fixed point is the identity, then the subset of G consisting of the derangements and the identity is a normal subgroup of G.

In purely group-theoretic language:

If G has a subgroup H such that H is self-normalizing and the intersection of any two different conjugates of H in G is trivial, then the subset of G consisting of the identity and the elements of G not contained in any conjugate of H form a subgroup of G.

This was proven by Frobenius using character theory, and still no proof has been given avoiding character theory. Character-free proofs exist when H is solvable or |H| is even. (Note that the Odd Order Theorem says that at least one of those is true for every finite group. But all known proofs of that theorem use character theory heavily.) DavidLHarden (talk) 08:20, 28 July 2010 (UTC)[reply]

OK, I'm having trouble. Which is the one that states that 2nd order linear differential equations about regular singular points have solutions of the form of an infinite power series multiplied by x^r? Perhaps slightly more information, perhaps slightly simpler information, is required on a disambiguation page if a diffyQ student can't find the article on one Frobenius's Theorem. --192.207.114.20 (talk) 23:38, 15 December 2012 (UTC)[reply]